One of the advantages of Hamiltonian mechanics is that it is similar in form to quantum mechanics, the theory that describes the motion of particles at very tiny (subatomic) distance scales. Here the ...One of the advantages of Hamiltonian mechanics is that it is similar in form to quantum mechanics, the theory that describes the motion of particles at very tiny (subatomic) distance scales. Here the Hamiltonian should be expressed as a function of position \(x\) and momentum \(p\) (rather than \(x\) and \(v\), as in the Lagrangian), so that \(H=H(x, p)\).
Hamiltonian mechanics can be used to describe simple systems such as a bouncing ball, a pendulum or an oscillating spring in which energy changes from kinetic to potential and back again over time, it...Hamiltonian mechanics can be used to describe simple systems such as a bouncing ball, a pendulum or an oscillating spring in which energy changes from kinetic to potential and back again over time, its strength is shown in more complex dynamic systems, such as planetary orbits in celestial mechanics. The more degrees of freedom the system has, the more complicated its time evolution.
